Reynolds Number Calculator

Calculate Reynolds number from mean flow speed, a clearly defined diameter, and either dynamic viscosity with density or kinematic viscosity directly. Convert SI and engineering units, follow the calculation, and check the approximate flow regime for a full circular pipe.

Formula and method

Reynolds number compares inertial effects with viscous effects. With mean cross-sectional speed V and characteristic diameter D:

Re = ρVD/μ = VD/ν, where ν = μ/ρ.

Density ρ is in kg/m³, dynamic viscosity μ in Pa·s, and kinematic viscosity ν in m²/s. The engine converts speed to m/s and diameter to m before calculating Re, which is dimensionless. Kinematic viscosity mode does not require density. Use property values at the same fluid composition, phase, temperature, and pressure.

Choose the correct diameter

• Circular pipe: use the actual internal diameter of the flow passage. Nominal pipe size and outside diameter are not interchangeable with internal diameter.
• Other fully filled ducts: choose hydraulic diameter and supply D_h = 4A/P_w, where A is the open flow area and P_w the wetted perimeter. For a full circular pipe this reduces to its internal diameter.
• The entered speed must be the mean speed through that same flow area, not the centerline speed. A hydraulic diameter does not make every duct behave like a circular pipe; geometry-specific correlations still apply.

Flow-regime guidance

These are engineering guides for ordinary internal circular-pipe flow, not universal transition guarantees. Inlet disturbances, roughness, and development affect transition. The calculator uses the unrounded result, treating only floating-point roundoff at a boundary as equality. Hydraulic-diameter mode reports Re without assigning a circular-pipe regime.

Assumptions and validity

• A single-phase Newtonian fluid with representative bulk properties and a fully filled flow passage. For non-Newtonian, multiphase, open-channel, or external flows, use the appropriate Reynolds definition and transition criteria.
• Speed must be nonnegative. Density, diameter, and the selected viscosity must be positive. Zero speed produces Re = 0 and is labeled “No flow.” Numerical overflow and nonzero underflow are rejected.
• Dynamic and kinematic viscosity are different quantities: 1 cP = 0.001 Pa·s; 1 cSt = 10⁻⁶ m²/s. They cannot be interchanged without density. Imperial dynamic viscosity here is mass-based lbm/(ft·s), not lbf·s/ft².
• No properties are looked up automatically. A Reynolds number alone does not calculate pressure drop, friction factor, entrance length, or a heat-transfer coefficient.

Worked example

Assume a fluid has density 1000 kg/m³ and dynamic viscosity 1 cP. It flows at a mean speed of 2 m/s through a pipe with actual internal diameter 50 mm. Convert μ = 0.001 Pa·s and D = 0.05 m.

Re = 1000 × 2 × 0.05 / 0.001 = 100,000. This falls in the turbulent circular-pipe guide range. Equivalently, ν = 0.001/1000 = 10⁻⁶ m²/s = 1 cSt, so Re = 2 × 0.05 / 10⁻⁶ = 100,000. These property values are illustrative assumptions, not a material-property dataset. Select “Load example” to reproduce the case.

Sources and calculation version

• NASA Glenn Research Center: Reynolds Number — definition, dimensionless interpretation, and ν = μ/ρ.
• Ansys Innovation Space: How can I tell whether my flow is laminar or turbulent? — internal-flow guide limits and their dependence on flow conditions.
• ASHRAE Terminology: duct and hydraulic diameter — flow-area/wetted-perimeter definition and the internal-diameter equivalence for a fully filled round duct.
• NIST SP 811, Appendix B.9 — length, mass, density, and dynamic/kinematic viscosity conversion factors.

Changelog: engine 1.0.0 introduces two viscosity methods, internal/hydraulic diameter bases, unit conversion, circular-pipe regime guidance, zero-flow handling, and input validation. Parameter source: your fluid and flow conditions; no property dataset is used. Engineering review status: independent review pending.